
Using the result of [1]}, we obtain a streaming algorithm that maintains a \((k,\epsilon )\) -coreset with negative weights for metric \(k\) -median requiring the storage of \(O(\epsilon ^{-2} k \log n)\)  points.

Given a \(O(k \cdot \text{poly}(\epsilon , \log n, \log (1/\delta )))\)  point \((k,\epsilon )\) -coreset, we would obtain a streaming algorithm that maintains a \((k,\epsilon )\) -coreset (with only positive weights) for metric \(k\) -median requiring the storage of \(O(k \cdot \text{poly}(\epsilon , \log n, \log (1/\delta )))\)  points. This differs from Theorem REF  in that the dependence on \(k\)  is linear instead of \(O(k \log k)\) .

